Interest problem solving

Johnny has 2 credit cards.

On Credit Card A, he has a balance of $16,000 at 3.99% fixed until that balance is paid off, and another $6600 at 10.99% (currently--the $6600 balance APR is variable pegged to Prime).
The card has a credit limit of $31,600, so Johnny has roughly $9000 available credit on Credit Card A. Any payments to Credit Card A are applied to the lowest APR rate first.

On Credit Card B, Johnny has a balance of roughly $5800, at 10.99% (currently--it is variable pegged to Prime). Credit Card B has a limit of $6000, which Johnny is nearing.

Johnny still needs to use credit cards to pay bills and necessities for a few months, and he should be able to pay off at least a third of his debt within the next few months, and all the remaining debt by the end of the year (roughly 6-7 months away.)

Credit Card A has a balance transfer offer of 0% APR for 18 months, at which time it reverts to the standard rate. There is a 3% fee for the transfer, but the fee is capped at $75.

Given all the above information, including the $75 transfer fee, Johnny's ability to pay all the debt within a year, the various rates of interest, the order in which payments are applied by the credit card companies (lowest APR first) etc., what is the mathematically correct plan for Johnny to undertake? Should he or should he not make use of the transfer, which card should he use for purchases if he doesn't, etc.

Show all math reasoning, now! If there is missing information necessary to complete the answer, please post that as well.

Yes, I am Johnny. I thought math guys would give the best, most accurate answer. Thanks in advance...